Question: ${\sqrt[3]{1250} = \text{?}}$
$\sqrt[3]{1250}$ is the number that, when multiplied by itself three times, equals $1250$ First break down $1250$ into its prime factorization and look for factors that appear three times. So the prime factorization of $1250$ is $2\times 5\times 5\times 5\times 5$ Notice that we can rearrange the factors like so: $1250 = 2 \times 5 \times 5 \times 5 \times 5 = (5\times 5\times 5) \times 2\times 5$ So $\sqrt[3]{1250} = \sqrt[3]{5\times 5\times 5} \times \sqrt[3]{2\times 5}$ $\sqrt[3]{1250} = 5 \times \sqrt[3]{2\times 5}$ $\sqrt[3]{1250} = 5 \sqrt[3]{10}$